The concept of plasticity describes the mechanisms that rearrange cerebral organization following a brain injury. During the last century, plasticity has been mainly investigated in humans with acute strokes. It was then shown: (i) that the brain is organized into highly specialized functional areas, often designated "eloquent" areas and (ii) that a lesion within the eloquent area gives rise to major irrevocable deficits. However, in sharp contrast with these observations, it was recently found that patients with low-grade gliomas were able to undergo massive cerebral resections without detectable functional consequence. In this paper, we tackle this puzzling observation and address the idea that brain plasticity cannot be fully understood and fruitfully studied without considering the temporal pattern of the injury inflicted to the brain. To achieve this goal, we first review experimental evidence showing that functional recovery is considerably better in the context of slow-growing injuries than after acute lesions. Both human and animal data are considered. In a second step, we emphasize that slow and acute lesions involve very different patterns of reorganization. In agreement with this idea, we show that the recruitment of remote brain areas in the ipsi- and contralesional hemispheres is much more efficient in slow growing than acute lesions. Finally in a last section, we briefly discuss the main implications of these results.